Sorry if this seems like a silly question, but I truly want to find out.
Is it possible for me to plug in my guitar and to have another cable going out into a real guitar amplifier(speaker)? Sorry if this doesn't make sense, but I just want to know if this headphone amplifier can be used like a FX pedal for guitars; you know, to add more of a dimension to the sound?

Don't really think this would be what you're looking for.
Any effect on your tone would be very small compared to any effects in your chain.
If anything it'll simply overload the circuits down your fx chain and you'll just get massive clipping.
If you want atmosphere at this price, get a strymon blue sky.
http://www.strymon.net/products/bluesky/

Don't expect great distorted/overdriven tone. It will probably have a clean tone, since its a headphone amp not designed for distortion. The impedence from 32 -600 would cause a mismatch, since most speakers run at 4, 8, 16 ohms. Even the clean tone might be mediocre without testing it first, if played through headphones.